### Find the best constant a

Give examples of events to show that these bounds cannot be improved (SEE ATTACHED).

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Give examples of events to show that these bounds cannot be improved (SEE ATTACHED).

K is a field, V is the vector space of all polynomials over K, D is the derivative function from V to V and g is a linear function from V to V given by g(f(x)) = xDf(x). Find all eigenvalues of g. When are there infinitely many eigenvalues? Please explain in detail. PLEASE NOTE: it states that g is a linear functio

Q1 Make the symbol indicated in brackets the subject of each formula shown express each in its simplest form. A. a+b+c-d-e [d] B. x=3y-t [y] C. c=2pi.r [r] D. f=9over5c+32 [c] E t=2pi square root l over g [l] q2. A formula used to calculate the power gain in an electronic amplifier in db is gain [g]=10log p2 over p1 wher

Is it possible for three planes to intersect in a single point?

By looking at the equation for a rational function, how can you tell if there will be "y-values" which never occur?

Find the horizontal asymptotes of each rational function. F(x) = 4x² + 1__ x² + x + 1

A chain is wrapped around a log. What pull will be necessary at an angle of 52 degrees to move the log at an effective rate of 234 N along the log? A cable is wrapped around a tree creating an angle of 49 degrees. The tension on each segment of the cable is 46 N. What is the resulting force on the tree?

A man's age at death was 1/29 of the year of his birth. How old was he in 1949? Hint: people rarely live past 100.

1.Determine the equation of the line through (-2, 0) with slope . Write the equation in standard form using only integers as the coefficients. 2.Determine the equation of the line through (0, 9) that is parallel to the line 3x + 5y = 15. Write the equation in slope-intercept form. 3.Determine the equation of the line th

Use the definition to show that the sequence (n-1)/(n+2) (n=1 to infinity) is Cauchy. Please show all steps.

See attached file for full problem description. Use the definition of convergence of a sequence to prove that the sequence (n-1)/(n+2) (n=1 to infinity) converges to 1. Please provide complete proof and explanation.

State the definition of a Cauchy sequence. Also, by negating this definition, state the definition of a sequence to be not Cauchy.

I need help finding the inverse of 3*2^(x-3)

Please advise what are the models/concepts. Thanks.

Use the phase line to predict the asymptotic (*see attachment*) behavior of the solution satisfying the specified initial condition ... *Please see attachment for complete question.

Please see the attached file for the fully formatted problems. ? Let S be a square, with vertices labelled (anticlockwise), 1,2,3,4. a symmetry of S is a rotation or reflection which preserves the square (although it may change the position of the vertices). Note that a symmetry is determined by its effect on the vertices.

A 20-foot board is cut into two pieces, Twice the length of the shorter piece is 4 ft more than the length of the longer piece. Find the length of the shorter piece.

An M&M has a volume of approximately 0.5 cm3. We have Avagadro's number of M&M's. The only place to store the M&M's in in Death Valley. The area of Death Valley is approximately 100miles2. How thick in miles would the layer of M&M's be?

Please assist me by solving the attached equations. Thanks.

4.76x^2 + 6.12x = -55.3 Find all real solutions, however i am getting a negative number, which is not workable?

I am supposed to find all real solutions: 1.5x^2 - 6.3x - 10.1 = 0 I am stuck, please see attachment

Can't figure out how to solve: x^2 + y^2 + 4y = 0 I need to graph the equation in a xy coordinate system.

X-2/x-6 = x-4/x-12

Show that the Diophantine equation x^2-y^2=n is solvable in integers if and only if n is odd or n is divisible by 4. When this equation is solvable, find all integer solutions.

0=-3,000 + 2500/(1+r)+ 1000/(1+r)^2 r=

The surface area of a right circular cylinder is given by the formula... (see attachment)

The surface area of a right circular cylinder is given by the formula S= 2*PIE SIGN*rh + 2*PIE SIGN* r^2, where r is the radius of the base, and h is the height of the cylinder. Solve the formula S= 2*PI*rh + 2*PI*r^2 for h.

Although Corollary 2 does not apply to the function 1 / (z — z_0) in the plane punctured at z_0, Theorem 6 can be used as follows to show that (see attached 1) for any circle C traversed once in the positive direction surrounding the point z_0. Introduce a horizontal branch cut from z_0 to infinity as in Fig. 4.25. In the r

The attached sequence of numbers is recursively defined. Please complete the sequence.

One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?